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Dynamic analysis of a biological economic model of prey-predator system with alternative prey

T. K. Kar, Bapan Ghosh

Abstract


The present paper deals with a differential algebraic, bioeconomic prey-predator model with distributed time delay and alternative food supply for predator. We discuss that the stability character of all the equilibrium points are unaffected by arbitrary time delay when economic profit is zero, and transcritical bifurcation occurs at an axial equilibrium point in that occasion. Indeed, the unique interior equilibrium point undergoes singularity induced bifurcation in zero economic profit case and a feedback control is designed to remove it. In contrast, a boundary equilibrium point also undergoes singularity induced bifurcation in zero economic profit case, but can’t be eliminated by the same. When economic rent is away from zero, Hopf-bifurcation is also investigated by treating time delay as the bifurcation parameter. Finally, numerical examples demonstrate the effectiveness of our analytical results and a fully numerical scheme is presented for the occurrence of saddle-node bifurcation at an interior equilibrium point regarding maximum profit as the bifurcation parameter.

Keywords


Prey-predator, distributed delay, transcritical bifurcation, singularity induced bifurcation, hopf-bifurcation, Feedback control.

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